Question

function a and function b are linear functions.
function a
x | y
-9 | -15
-4 | -5
7 | 17
function b
graph of a line
which statement is true?
the y-intercept of function a is greater than the y-intercept of function b.
the y-intercept of function a is less than the y-intercept of function b.

Explanation:

Step1: Find slope of Function A

Use two points from Function A's table, e.g., \((-9, -15)\) and \((-4, -5)\).
Slope \(m_A = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - (-15)}{-4 - (-9)} = \frac{10}{5} = 2\).

Step2: Equation of Function A

Use point - slope form \(y - y_1 = m(x - x_1)\) with \((-4, -5)\):
\(y - (-5) = 2(x - (-4))\)
\(y + 5 = 2(x + 4)\)
\(y + 5 = 2x + 8\)
\(y = 2x + 3\).
So, \(y\) - intercept of Function A is \(3\) (when \(x = 0\), \(y = 3\)).

Step3: Find \(y\) - intercept of Function B

From the graph, Function B passes through \((0, -1)\) (since it crosses the \(y\) - axis at \(x = 0\), \(y=-1\)).

Step4: Compare \(y\) - intercepts

\(y\) - intercept of A: \(3\); \(y\) - intercept of B: \(-1\).
Since \(3>-1\), the \(y\) - intercept of Function A is greater than that of Function B.

Answer:

The \(y\) - intercept of Function A is greater than the \(y\) - intercept of Function B.